\(\mathcal {V}\)

Set of all agents

\(\mathcal {L}\)

Set of all locations

N

Number of agents in the system

L

Number of locations in the system

n

Number of agents in each location

D

Side of the square planar space

T

Total number of discrete timesteps in the observation window

t

Index for discrete time instants

ℓ

Index for the locations in the system

i,j

Indices for the agents in the system

ρ_{ℓ}

Density of location ℓ in the system

β(i)

Function that maps agent i to its base location

Ω_{ℓ}

Region of space occupied by location ℓ

x_{i}(t),y_{i}(t)

Position occupied by agent i in the planar space at time t

θ_{i}(t)

Direction of the motion of agent i at time t

Φ_{i}(t)

Angle of the direction of the shortest path from x_{i}(t),y_{i}(t) to Ω_{β(i)}

Δθ_{it}

Angle drawn uniformly at random in [0,2π) for agent i at time t

v

Velocity of agents outside their base location

α

Randomness in the agents’ motion toward their base location

p

Probability of jumping outside the base location

P_{jump}(d)

Probability of jumping at a distance d from the base location

q_{in}

Probability of being inside the base location

q_{out}

Probability of being outside the base location

q_{ℓ}

Probability of being inside Ω_{ℓ}

q_{out,d}

Probability of being at a distance d from the closest location

Ψ_{in},Ψ_{out},Ψ_{d}

Probability that agents are inside, outside, and at a distance d


from their base location

P(Σ)

Probability density function of locations’ radii

γ

Exponents of the power law distribution of locations’ radii

Σ_{min},Σ_{max}

Lower and higher cutoff of the distribution of locations’ radii

G(σ)

Probability density function of agents’ radii of interaction

ω

Exponents of the power law distribution of radii of interaction

σ_{min},σ_{max}

Lower and higher cutoff of the distribution of radii of interaction

k_{i}

Degree of agent i

λ

Infection probability per contact

μ

Recovery probability per unit time

s(t),i(t),r(t)

Fraction of susceptible, infected, and recovered agents in the system

s_{ℓ}(t),i_{ℓ}(t),r_{ℓ}(t)

Fraction of susceptible, infected, and recovered agents in Ω_{ℓ}

s_{out,d}(t),i_{out,d}(t),r_{out,d}(t)

Fraction of susceptible, infected, and recovered agents at distance d


from the closest location

Λ_{ℓ}(t)

Contagion probability in Ω_{ℓ}

Λ_{out,d}(t)

Contagion probability at a distance d from the closest location

〈·〉

Statistical average of the quantity “ ·”

E [·]

Expected value of the quantity “ ·”

P[·]

Probability of an event “ ·”
